It sounds silly to ask that about the American League Player of the Month, but go ahead, ask it. Peter Bjarkman, who writes for the website baseballdecuba.com and has traveled extensively with Cuba's national team, has a quick answer.

"I will go on record as saying that his April stats may be the lowest of any month of the season," Bjarkman said Tuesday. "I think he has a real shot at breaking [Mark] McGwire's rookie home run record of 49."

While Gordon Beckham led the White Sox to a 5-1 victory over the Cubs on a 46-degree night at Wrigley Field, Abreu was 1-for-4 with a double. He is leading the Majors with 12 home runs and is second to Giancarlo Stanton with 35 RBIs -- totals that project to 57 and 167 over a full season.

No one should expect Abreu to maintain that pace, but as far as pure hitting and overall production, it's worth considering a couple of factors:

• Abreu was a true Triple Crown hitter for the Cienfuegos Elephants, hitting for a high average as well as for power, and his early batting average (.254) has been ordinary. His strikeout/walk ratio and on-base percentage aren't where those who know him expect them to be.

• Abreu has put up his eye-popping totals while surviving an unusually cold spring in Chicago, where the early-season weather is always a challenge for hitters. Conversely, the ball flies at U.S. Cellular Field once the thermometer gets to 80 degrees. In fact, it was the best park in the Major Leagues for right-handed power hitters over the last three seasons, according to Bill James' Ballpark Indexes.

When Robin Ventura says "the sky's the limit" for his 27-year-old rookie, he's on the money. The landscape sets up well for Abreu to improve in many ways.

Bjarkman says he talked about exactly that with Abreu when he visited U.S. Cellular last week.

"It is my feeling precisely," Bjarkman said. "[Jose] is a warm-weather hitter, and I have been saying to everyone, 'Just wait until July and August.' "

Ventura also believes that Abreu has demonstrated only some of his skills as a hitter.

"You're always hesitant to say, 'This guy could be so much better,' when a guy's on such a great start," Ventura said. "But there are things he's going to learn that are going to make him better. He'll learn in certain situations that they're going to pitch around him. Right now, he's looking to knock guys in. Eventually, he's going to learn what they're trying to do and become more selective."

In Monday night's extra-inning victory over the Cubs, Abreu laid off two borderline sliders to work a ninth-inning walk from Jeff Samardzija. He took a walk rather than swinging for the ivy, and it put the go-ahead run on first base with one out.

"It's easy when you sit over here and you think, 'Oh, he's going to throw a slider,'" Ventura said. "But when you're the one with your feet in the box and everyone else thinks he's going to throw a slider and then he doesn't throw a slider, you're the one who looks bad. He makes adjustments. He's learning. It's all part of it. At the end of the game, that's a big [plate appearance] for us. It gave us an opportunity. That's good stuff."

Abreu went into Tuesday night's game ranked 53rd in the AL in batting average and 65th in on-base percentage. He has only seven unintentional walks to offset 37 strikeouts in 134 at-bats.

This is a guy who batted .412 for a three-season stretch in Cuba, including .453 in 2011 (the epic performance in which Abreu hit 33 home runs in 66 games). He had more walks than strikeouts in each of his last four seasons with Cienfuegos.

Abreu seemed sheepish after swinging at the first three pitches he saw from the Twins' Ricky Nolasco on Opening Day, even though he lined one for a double and another for a single. He said he doesn't usually attack the first pitch but was excited. Abreu has seemed that way at other times, and why not?

Abreu is going to settle down and raise his batting average and OBP, and no one should be shocked if he's in the top 10 in those categories next season.

"I do see him as a .300 hitter, making adjustments," Ventura said. "Sky's the limit is a pretty broad thing to put on him, but he's just a good player. There's going to be different things he learns about the game, that he's going to get better [doing]. It doesn't necessarily mean he's going to hit .450, but he's going to probably be a better defender, runner, [have more] plate discipline, not strike out as much."

Ventura spent 10 of his 16 Major League seasons based in Chicago. He knew the shock that would face a newcomer from Cuba when he left the warm weather of Arizona for the Midwest spring, but didn't want to alarm Abreu.

"You do get a little concerned," Ventura said. "You know what it can be like. I don't think he had any idea, and we weren't really going to give him any information on how cold the winter really was and how cold it could be in April and May. But he's been through it [now]. Part of [our excitement] is he's gone through April, where it hasn't been very warm and our ballpark isn't really a hitter's ballpark, and he's been able to put up the numbers he has. That's a good sign for me. Most guys try to make it through April with your head above water, and then you make hay in June, July and August."

The White Sox have played 18 of their games in Chicago, including eight when the game-time temperature was 37-48 degrees. Abreu has been a minimal factor in all but one of those games, combining to go 5-for-30 with no home runs and four RBIs. He was also 0-for-8 in two games in that temperature range on the road, one in Kansas City and another in Colorado.

Eliminate those meat-locker games and Abreu is hitting .302 with a home run every eight at-bats.

Sure, the Major League numbers represent a small sample size. But this is a guy with a big body of work, not some piece of work with a big body.

Abreu will be the toast of U.S. Cellular Field on Wednesday night, and that's not even the best part for him. The forecast calls for 72 degrees at game time.